Abstract.This paper employs Fisher's model of adaptation to understand the expected
fitness effect of fixing a mutation in a natural population. Fisher's model
in one dimension admits a closed form solution for this expected fitness
effect. A combination of different parameters, including the distribution
of mutation lengths, population sizes, and the initial state that the
population is in, are examined to see how they affect the expected fitness
effect of state transitions. The results show that the expected fitness
change due to the fixation of a mutation is always positive, regardless
of the distributional shapes of mutation lengths, effective population
sizes, and the initial state that the population is in. The further away
the initial state of a population is from the optimal state, the slower
the population returns to the optimal state. Effective population size
(except when very small) has little effect on the expected fitness change
due to mutation fixation. The always positive expected fitness change
suggests that small populations may not necessarily be doomed due to the
runaway process of fixation of deleterious mutations.